The only thing I can think of is I have a script run every 30 minutes which scans a folder for Plex (check for recently added items).
I have suspended the script for now and will test to see if that is causing the slowness.

Looks like handbrake has an issue. Try downloading the latest nightly build of 64 bit CLI handbrake and replace it on the mcebuddy handbrake directory. Let me know if that solves the issue. Do you still have the original file for this conversion to retest?

Replaced CLI file.
I recorded a different show and sent it through MCEBuddy. It converted cleanly with no delay.
I'll let you know the result when Fallon records again tonight.
Thank you for your assistance. VERY helpful.